prime_positive_bounded_product_coprime

Exact expanded PA statement

forall p b c l F. ((~(p = 1) /\ forall frp_prime_left_prime_product_prime frp_prime_right_prime_product_prime. p = frp_prime_left_prime_product_prime * frp_prime_right_prime_product_prime -> frp_prime_left_prime_product_prime = 1 \/ frp_prime_right_prime_product_prime = 1)) -> (forall fppc_index_prime_product_bounds fppc_factor_prime_product_bounds. (exists frp_gap_prime_product_bounds_index_bound. frp_gap_prime_product_bounds_index_bound + S fppc_index_prime_product_bounds = l) -> (((exists ff_h_fppc_prime_product_bounds_decoded. ff_h_fppc_prime_product_bounds_decoded + S (fppc_factor_prime_product_bounds) = S ((S (fppc_index_prime_product_bounds)) * c)) /\ exists ff_q_fppc_prime_product_bounds_decoded. b = ff_q_fppc_prime_product_bounds_decoded * S ((S (fppc_index_prime_product_bounds)) * c) + (fppc_factor_prime_product_bounds))) -> (~(fppc_factor_prime_product_bounds = 0) /\ (exists frp_gap_prime_product_bounds_factor_bound. frp_gap_prime_product_bounds_factor_bound + S fppc_factor_prime_product_bounds = p))) -> (exists ff_u_prime_product_product ff_v_prime_product_product. ((((exists ff_h_prime_product_product_start. ff_h_prime_product_product_start + S (1) = S ((S (0)) * ff_v_prime_product_product)) /\ exists ff_q_prime_product_product_start. ff_u_prime_product_product = ff_q_prime_product_product_start * S ((S (0)) * ff_v_prime_product_product) + (1))) /\ ((((exists ff_h_prime_product_product_terminal. ff_h_prime_product_product_terminal + S (F) = S ((S (l)) * ff_v_prime_product_product)) /\ exists ff_q_prime_product_product_terminal. ff_u_prime_product_product = ff_q_prime_product_product_terminal * S ((S (l)) * ff_v_prime_product_product) + (F))) /\ forall ff_i_prime_product_product. (exists ff_lt_prime_product_product_bound. ff_lt_prime_product_product_bound + S ff_i_prime_product_product = l) -> exists ff_p_prime_product_product ff_r_prime_product_product ff_s_prime_product_product. ((((exists ff_h_prime_product_product_factor. ff_h_prime_product_product_factor + S (ff_p_prime_product_product) = S ((S (ff_i_prime_product_product)) * c)) /\ exists ff_q_prime_product_product_factor. b = ff_q_prime_product_product_factor * S ((S (ff_i_prime_product_product)) * c) + (ff_p_prime_product_product))) /\ ((((exists ff_h_prime_product_product_partial. ff_h_prime_product_product_partial + S (ff_r_prime_product_product) = S ((S (ff_i_prime_product_product)) * ff_v_prime_product_product)) /\ exists ff_q_prime_product_product_partial. ff_u_prime_product_product = ff_q_prime_product_product_partial * S ((S (ff_i_prime_product_product)) * ff_v_prime_product_product) + (ff_r_prime_product_product))) /\ ((((exists ff_h_prime_product_product_successor. ff_h_prime_product_product_successor + S (ff_s_prime_product_product) = S ((S (S ff_i_prime_product_product)) * ff_v_prime_product_product)) /\ exists ff_q_prime_product_product_successor. ff_u_prime_product_product = ff_q_prime_product_product_successor * S ((S (S ff_i_prime_product_product)) * ff_v_prime_product_product) + (ff_s_prime_product_product))) /\ ff_s_prime_product_product = ff_r_prime_product_product * ff_p_prime_product_product)))))) -> (forall frp_divisor_prime_product_result. (exists frp_left_factor_prime_product_result. F = frp_divisor_prime_product_result * frp_left_factor_prime_product_result) -> (exists frp_right_factor_prime_product_result. p = frp_divisor_prime_product_result * frp_right_factor_prime_product_result) -> frp_divisor_prime_product_result = 1)